During the process of mask write or direct write, several factors contribute to induce errors and prevent the achievement of the expected pattern fidelity. Some of these factors are the electron scattering (forward and backward), resist diffusion, resist thickness, etching, flare, fogging, metrology, heating, etc. In order to improve the resolution and reduce the impact of these phenomena, there are several strategies of proximity effect correction (PEC), fogging effect correction (FEC), etching compensation, among others. The strategies are based on a prediction of the impact of each effect followed by a correction of these by means of dose and/or geometry compensation. Therefore, the quality of the correction depends upon the quality of the models used to predict the phenomena, said models being different from one manufacturing process to another. High accuracy of the model and of the corrections can certainly be obtained, but at a high computation cost.
It has become common knowledge to use a decomposition of the model into two models, a first one to predict the electronic proximity effects, and a second one to predict all the other effects, often called resist model.
In the art, prediction of the electronic proximity effects is carried out using one or more Point Spread Function (PSF) of different types (Gaussian or other) which are convoluted with the target design to give an aerial image at the resist level.
The parameters of the resist model have also to be calculated from the characteristics of the target design, so that the model accurately represents the threshold for the various pattern configurations in the design. The resist model should be capable, at the same, of correcting the imperfections of the electronic model and of representing the impact of the other steps of the manufacturing process, notably the effects of the exposure process as well as the resist development.
A plurality of models have been disclosed and used, to define an adequate resist model, notably:
Type I models: they are characterized by a constant energy threshold, wherein the constant energy threshold is deemed to define a level of energy above which the interaction of the beam with the resist reveals the pattern (in the case of negative resists);
Type II models: they are characterized by a combination of a constant energy threshold, defined as above, with a variable bias which is defined on the contours of each sub-part of the target design as a polynomial function of the local, semi-global or global properties of the aerial image; examples of these Type II models are disclosed by Dunn et alii, (2009) “Etch Aware Optical Proximity Correction: A First Step Toward Integrated Pattern Engineering”, Optical Microlithography XXII, proc. SPIE vol 7274; Q. Liu et alii (2010). “Study of Model based etch bias retarget for OPC”, Optical Microlithography) (XII, proc SPIE vol 7640; J.-G. Park et alii (2011), ‘The effective etch process proximity correction methodology for improving on chip CD variation in 20 nm node DRAM gate’, Design for Manufacturability though Design-Process Integration V, proc. SPIE vol 7974; in the models of these Type II, the parameters which are taken into account to compute the bias are the size of the design, the space between parts of the design or the density of the design;
Type III models: these models correspond to another formulation, based on a variable energy threshold using parameters and functions of the same type as the Type II models; a disclosure of this Type III models can be found in “Cobb, N. B.; Zakhor, A.; Reihani, M.; Jahansooz, F. & Raghavan, V. N. Experimental results on optical proximity correction with variable-threshold resist model Proc. SPIE, 1997, 3051, 458-46” Models of Type I have been found not to be accurate enough, especially for some critical patterns, because a constant energy threshold does not represent all the physical effects on the target surface.
Models of Type II and Type III have been demonstrated by experimental use by the applicant as not working in a generality of cases. This is because a polynomial representation may not cover all experimental behaviors. Although the variables which are selected work accurately enough for some parts of the design patterns, they may not work for others, where they do no bring any improvement to the representation of the physical properties and may also lead to worsening the scenario. Also, it might be interesting in some situations to use one model instead of two different models to represent the electronic effects and the process effects, such a combination being time consuming.